Estimating the Strength of an Association Based on a Robust Smoother

It is known that the more obvious parametric approaches to fitting a regression line to data are often not flexible enough to provide an adequate approximation of the true regression line. Many nonparametric regression estimators, often called smoothers, have been derived that are aimed at dealing with this problem. The paper deals with the issue of estimating the strength of an association based on the fit obtained by a robust smoother. A simple approach, already known, is to estimate explanatory power in a fairly obvious manner. This approach has been found to perform reasonably well when using the smoother LOESS. But when using a running interval, which provides a simple way of using any robust measure of location, the method performs poorly, even with a reasonably large sample size. The paper suggests an alternative estimation method that performs much better in simulations.